共查询到20条相似文献,搜索用时 991 毫秒
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在本文中先给出了弧元素、面元索在坐标变换下的变换公式,然后给出了曲线、曲面积分在坐标变换下的变换公式,最后利用上述坐标变换公式推出了曲线曲面积分的对称性质. 相似文献
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正交变换在曲线、曲面积分计算中的应用林元重(江西萍乡高等专科学校337055)对于三维空间的曲线积分与曲面积分,如果知道其积分曲线或积分曲面的参数形式,一般可按数学分析教材所介绍的公式计算.但是,对于某些曲线、曲面积分,要把积分曲线或曲面用适当的参数... 相似文献
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格林公式、高斯公式和斯托克斯公式揭示了曲线积分、曲面积分和重积分三者的关系,因此在解题中可依此三个公式将问题进行转化,这样又增加了一种解题的方法,但必须注意转化的条件. 相似文献
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从一个具体的物理问题入手,探讨了如何将第一类曲面积分转化为两个第一类曲线积分的累次形式,从而给出了这两类积分之间的关系,并通过举例说明该公式可以用来直观简便地计算第一类曲面积分. 相似文献
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In this paper we obtain some formulas for totally umbilical hypersurfaces in a locally symmetric manifold, and derive some local results on the hypersurfaces from these formulas. 相似文献
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Gil Solanes 《Transactions of the American Mathematical Society》2006,358(3):1105-1115
We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.
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该文对 anti-de Sitter 空间H1n+1中的紧致类空超曲面建立了积分公式,并应用它们在常高阶平均曲率的条件下讨论了H1n+1中紧致类空超曲面的全脐问题. 相似文献
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Vittorio Martino 《复变函数与椭圆型方程》2018,63(3):360-367
We show some integral formulas involving the characteristic curvature for closed real hypersurfaces in complex spaces. 相似文献
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We obtain some new formulas for convex hypersurfaces in a space form. 相似文献
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在n+1维静态AdS时空(M)中,利用双扭结构建立了一些积分公式,并利用这些积分公式证得:如果(M)的Ricci曲率具有非负离差,那么以n-1维圆球面为边界的常平均曲率类空超曲面必为测地圆盘(h=0)或全脐盖(h≠0).作为推论,对于离差为零的Einstein静态AdS时空,结论也真. 相似文献
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《数学季刊》2017,(4)
In this paper, firstly using different method and technique we derive the corresponding integral representation formulas of(0, q)(q 0) differential forms for the two types of the bounded domains in complex submanifolds with codimension-m. Secondly we obtain the unified integral representation formulas of(0, q)(q 0) differential forms for the general bounded domain in complex submanifold with codimension-m, which include Hatziafratis formula, i.e. Koppelman type integral formula for the bounded domain with smooth boundary in analytic varieties. In particular, when m = 0, we obtain the unified integral representation formulas of(0, q)(q 0) differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula. 相似文献
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Eduardo Gallego 《Differential Geometry and its Applications》2005,22(3):315-325
Using results from integral geometry, we find inequalities involving mean curvature integrals of convex hypersurfaces in hyperbolic space. Such inequalities generalize the Minkowski formulas for euclidean convex sets. 相似文献
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We obtain new upper bounds for the number of integral solutionsof a complete system of symmetric equations, which may be viewedas a multi-dimensional version of the system considered in Vinogradov'smean value theorem. We then use these bounds to obtain Weyl-typeestimates for an associated exponential sum in several variables.Finally, we apply the HardyLittlewood method to obtainasymptotic formulas for the number of solutions of the Vinogradov-typesystem and also of a related system connected to the problemof finding linear spaces on hypersurfaces. 2000 MathematicsSubject Classification 11D45, 11D72, 11L07, 11P55. 相似文献
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邱春晖 《数学物理学报(A辑)》2001,21(4):485-491
利用权因子,我们得到了复流形上边界不必光滑的强拟凸域上(狆,狇)微分形式的带权因子的Koppelman Leray公式及其 方程的带权因子的解,其特点是不含有边界积分,从而避免了边界积分的复杂估计.其次,引进了权因子,带权因子的积分公式在应用上具有更大的灵活性. 相似文献